JEE Main 2021 (Online) 26th February Morning ShiftQuestion 1
If $(1,5,35)$, $(7,5,5)$, $(1,\lambda,7)$ and $(2\lambda,1,2)$ are coplanar, then the sum of all possible values of $\lambda$ is :
3D Geometry
Solution
Coplanarity: determinant of $(6,0,-30)$, $(0,\lambda-5,-28)$, $(2\lambda-1,-4,-33)$ is $60\lambda^2-528\lambda+468=0$, i.e. $5\lambda^2-44\lambda+39=0$. Sum of roots $=\frac{44}5$.